Class 12 Determinants · Case Study4 Marksmatrix_method_applications
Class 12 Maths · Determinants · Case Study #35
A coaching institute has two fee categories: standard and subsidised. Section A has 5 standard-fee and 20 subsidised-fee students, collecting ₹9,000 monthly. Section B has 25 standard-fee and 5 subsidised-fee students, collecting ₹26,000. Let x,y be the respective monthly fees.
Part (1) 1 Marks
Write the linear equations.
Answer: 5x+20y=9000; 25x+5y=26000.
- Multiply the student count in each fee category by that category’s fee, and add within each section.
- The equations are 5x+20y=9000 and 25x+5y=26000.
Part (2) 1 Marks
Express the system as AX=B.
Answer: [[5,20],[25,5]][x,y]ᵀ=[9000,26000]ᵀ.
- The two coefficient rows are [5,20] and [25,5].
- Thus \(\begin{bmatrix}5 & 20\\25 & 5\end{bmatrix}\)[x,y]ᵀ=[9000,26000]ᵀ.
Part (3) 2 Marks
Find the two monthly fees.
Answer: Standard fee ₹1,000; subsidised fee ₹200.
- The coefficient determinant is 25−500=−475≠0. Its inverse is (−1/475)[[5,−20],[−25,5]].
- Multiply by [9000,26000]ᵀ: (−1/475)[45000−520000,−225000+130000]ᵀ=[1000,200]ᵀ.
- Therefore standard and subsidised monthly fees are ₹1,000 and ₹200 respectively.